Warning

This documents an unmaintained version of NetworkX. Please upgrade to a maintained version and see the current NetworkX documentation.

# Source code for networkx.classes.function

"""Functional interface to graph methods and assorted utilities.
"""
#    Aric Hagberg <hagberg@lanl.gov>
#    Dan Schult <dschult@colgate.edu>
#    Pieter Swart <swart@lanl.gov>
#
import networkx as nx
from networkx.utils import not_implemented_for
import itertools
__author__ = """\n""".join(['Aric Hagberg (hagberg@lanl.gov)',
'Pieter Swart (swart@lanl.gov)',
'Dan Schult(dschult@colgate.edu)'])
__all__ = ['nodes', 'edges', 'degree', 'degree_histogram', 'neighbors',
'number_of_nodes', 'number_of_edges', 'density',
'nodes_iter', 'edges_iter', 'is_directed','info',
'freeze','is_frozen','subgraph','create_empty_copy',
'set_node_attributes','get_node_attributes',
'set_edge_attributes','get_edge_attributes',
'all_neighbors','non_neighbors', 'non_edges',
'common_neighbors']

[docs]def nodes(G):
"""Return a copy of the graph nodes in a list."""
return G.nodes()

[docs]def nodes_iter(G):
"""Return an iterator over the graph nodes."""
return G.nodes_iter()

[docs]def edges(G,nbunch=None):
"""Return list of  edges adjacent to nodes in nbunch.

Return all edges if nbunch is unspecified or nbunch=None.

For digraphs, edges=out_edges
"""
return G.edges(nbunch)

[docs]def edges_iter(G,nbunch=None):
"""Return iterator over  edges adjacent to nodes in nbunch.

Return all edges if nbunch is unspecified or nbunch=None.

For digraphs, edges=out_edges
"""
return G.edges_iter(nbunch)

[docs]def degree(G,nbunch=None,weight=None):
"""Return degree of single node or of nbunch of nodes.
If nbunch is ommitted, then return degrees of *all* nodes.
"""
return G.degree(nbunch,weight)

def neighbors(G,n):
"""Return a list of nodes connected to node n. """
return G.neighbors(n)

[docs]def number_of_nodes(G):
"""Return the number of nodes in the graph."""
return G.number_of_nodes()

[docs]def number_of_edges(G):
"""Return the number of edges in the graph. """
return G.number_of_edges()

[docs]def density(G):
r"""Return the density of a graph.

The density for undirected graphs is

.. math::

d = \frac{2m}{n(n-1)},

and for directed graphs is

.. math::

d = \frac{m}{n(n-1)},

where n is the number of nodes and m  is the number of edges in G.

Notes
-----
The density is 0 for a graph without edges and 1 for a complete graph.
The density of multigraphs can be higher than 1.

Self loops are counted in the total number of edges so graphs with self
loops can have density higher than 1.
"""
n=number_of_nodes(G)
m=number_of_edges(G)
if m==0 or n <= 1:
d=0.0
else:
if G.is_directed():
d=m/float(n*(n-1))
else:
d= m*2.0/float(n*(n-1))
return d

[docs]def degree_histogram(G):
"""Return a list of the frequency of each degree value.

Parameters
----------
G : Networkx graph
A graph

Returns
-------
hist : list
A list of frequencies of degrees.
The degree values are the index in the list.

Notes
-----
Note: the bins are width one, hence len(list) can be large
(Order(number_of_edges))
"""
degseq=list(G.degree().values())
dmax=max(degseq)+1
freq= [ 0 for d in range(dmax) ]
for d in degseq:
freq[d] += 1
return freq

[docs]def is_directed(G):
""" Return True if graph is directed."""
return G.is_directed()

def frozen(*args):
"""Dummy method for raising errors when trying to modify frozen graphs"""
raise nx.NetworkXError("Frozen graph can't be modified")

[docs]def freeze(G):
"""Modify graph to prevent further change by adding or removing
nodes or edges.

Node and edge data can still be modified.

Parameters
-----------
G : graph
A NetworkX graph

Examples
--------
>>> G=nx.Graph()
>>> G=nx.freeze(G)
>>> try:
... except nx.NetworkXError as e:
...    print(str(e))
Frozen graph can't be modified

Notes
-----
To "unfreeze" a graph you must make a copy by creating a new graph object:

>>> graph = nx.path_graph(4)
>>> frozen_graph = nx.freeze(graph)
>>> unfrozen_graph = nx.Graph(frozen_graph)
>>> nx.is_frozen(unfrozen_graph)
False

--------
is_frozen
"""
G.remove_node=frozen
G.remove_nodes_from=frozen
G.remove_edge=frozen
G.remove_edges_from=frozen
G.clear=frozen
G.frozen=True
return G

[docs]def is_frozen(G):
"""Return True if graph is frozen.

Parameters
-----------
G : graph
A NetworkX graph

--------
freeze
"""
try:
return G.frozen
except AttributeError:
return False

def subgraph(G, nbunch):
"""Return the subgraph induced on nodes in nbunch.

Parameters
----------
G : graph
A NetworkX graph

nbunch : list, iterable
A container of nodes that will be iterated through once (thus
it should be an iterator or be iterable).  Each element of the
container should be a valid node type: any hashable type except
None.  If nbunch is None, return all edges data in the graph.
Nodes in nbunch that are not in the graph will be (quietly)
ignored.

Notes
-----
subgraph(G) calls G.subgraph()
"""
return G.subgraph(nbunch)

[docs]def create_empty_copy(G,with_nodes=True):
"""Return a copy of the graph G with all of the edges removed.

Parameters
----------
G : graph
A NetworkX graph

with_nodes :  bool (default=True)
Include nodes.

Notes
-----
Graph, node, and edge data is not propagated to the new graph.
"""
H=G.__class__()
if with_nodes:
return H

[docs]def info(G, n=None):
"""Print short summary of information for the graph G or the node n.

Parameters
----------
G : Networkx graph
A graph
n : node (any hashable)
A node in the graph G
"""
info='' # append this all to a string
if n is None:
info+="Name: %s\n"%G.name
type_name = [type(G).__name__]
info+="Type: %s\n"%",".join(type_name)
info+="Number of nodes: %d\n"%G.number_of_nodes()
info+="Number of edges: %d\n"%G.number_of_edges()
nnodes=G.number_of_nodes()
if len(G) > 0:
if G.is_directed():
info+="Average in degree: %8.4f\n"%\
(sum(G.in_degree().values())/float(nnodes))
info+="Average out degree: %8.4f"%\
(sum(G.out_degree().values())/float(nnodes))
else:
s=sum(G.degree().values())
info+="Average degree: %8.4f"%\
(float(s)/float(nnodes))

else:
if n not in G:
raise nx.NetworkXError("node %s not in graph"%(n,))
info+="Node % s has the following properties:\n"%n
info+="Degree: %d\n"%G.degree(n)
info+="Neighbors: "
info+=' '.join(str(nbr) for nbr in G.neighbors(n))
return info

[docs]def set_node_attributes(G, name, values):
"""Set node attributes from dictionary of nodes and values

Parameters
----------
G : NetworkX Graph

name : string
Attribute name

values: dict
Dictionary of attribute values keyed by node. If values is not a
dictionary, then it is treated as a single attribute value that is then
applied to every node in G.

Examples
--------
>>> G = nx.path_graph(3)
>>> bb = nx.betweenness_centrality(G)
>>> nx.set_node_attributes(G, 'betweenness', bb)
>>> G.node['betweenness']
1.0
"""
try:
values.items
except AttributeError:
# Treat value as the attribute value for each node.
values = dict(zip(G.nodes(), [values] * len(G)))

for node, value in values.items():
G.node[node][name] = value

[docs]def get_node_attributes(G, name):
"""Get node attributes from graph

Parameters
----------
G : NetworkX Graph

name : string
Attribute name

Returns
-------
Dictionary of attributes keyed by node.

Examples
--------
>>> G=nx.Graph()
>>> color=nx.get_node_attributes(G,'color')
>>> color
'red'
"""
return dict( (n,d[name]) for n,d in G.node.items() if name in d)

[docs]def set_edge_attributes(G, name, values):
"""Set edge attributes from dictionary of edge tuples and values.

Parameters
----------
G : NetworkX Graph

name : string
Attribute name

values : dict
Dictionary of attribute values keyed by edge (tuple). For multigraphs,
the keys tuples must be of the form (u, v, key). For non-multigraphs,
the keys must be tuples of the form (u, v). If values is not a
dictionary, then it is treated as a single attribute value that is then
applied to every edge in G.

Examples
--------
>>> G = nx.path_graph(3)
>>> bb = nx.edge_betweenness_centrality(G, normalized=False)
>>> nx.set_edge_attributes(G, 'betweenness', bb)
>>> G['betweenness']
2.0

"""
try:
values.items
except AttributeError:
# Treat value as the attribute value for each edge.
if G.is_multigraph():
edges = G.edges(keys=True)
else:
edges = G.edges()
values = dict(zip(edges, [values] * len(edges)))

if G.is_multigraph():
for (u, v, key), value in values.items():
G[u][v][key][name] = value
else:
for (u, v), value in values.items():
G[u][v][name] = value

[docs]def get_edge_attributes(G, name):
"""Get edge attributes from graph

Parameters
----------
G : NetworkX Graph

name : string
Attribute name

Returns
-------
Dictionary of attributes keyed by edge. For (di)graphs, the keys are
2-tuples of the form: (u,v). For multi(di)graphs, the keys are 3-tuples of
the form: (u, v, key).

Examples
--------
>>> G=nx.Graph()
>>> color=nx.get_edge_attributes(G,'color')
>>> color[(1,2)]
'red'
"""
if G.is_multigraph():
edges = G.edges(keys=True, data=True)
else:
edges = G.edges(data=True)
return dict( (x[:-1], x[-1][name]) for x in edges if name in x[-1] )

[docs]def all_neighbors(graph, node):
""" Returns all of the neighbors of a node in the graph.

If the graph is directed returns predecessors as well as successors.

Parameters
----------
graph : NetworkX graph
Graph to find neighbors.

node : node
The node whose neighbors will be returned.

Returns
-------
neighbors : iterator
Iterator of neighbors
"""
if graph.is_directed():
values = itertools.chain.from_iterable([graph.predecessors_iter(node),
graph.successors_iter(node)])
else:
values = graph.neighbors_iter(node)

return values

[docs]def non_neighbors(graph, node):
"""Returns the non-neighbors of the node in the graph.

Parameters
----------
graph : NetworkX graph
Graph to find neighbors.

node : node
The node whose neighbors will be returned.

Returns
-------
non_neighbors : iterator
Iterator of nodes in the graph that are not neighbors of the node.
"""
nbors = set(neighbors(graph, node)) | set([node])
return (nnode for nnode in graph if nnode not in nbors)

[docs]def non_edges(graph):
"""Returns the non-existent edges in the graph.

Parameters
----------
graph : NetworkX graph.
Graph to find non-existent edges.

Returns
-------
non_edges : iterator
Iterator of edges that are not in the graph.
"""
if graph.is_directed():
for u in graph.nodes_iter():
for v in non_neighbors(graph, u):
yield (u, v)
else:
S = set()
for u in graph.nodes_iter():
for v in non_neighbors(graph, u):
if (u, v) not in S:
yield (u, v)

@not_implemented_for('directed')
[docs]def common_neighbors(G, u, v):
"""Return the common neighbors of two nodes in a graph.

Parameters
----------
G : graph
A NetworkX undirected graph.

u, v : nodes
Nodes in the graph.

Returns
-------
cnbors : iterator
Iterator of common neighbors of u and v in the graph.

Raises
------
NetworkXError
If u or v is not a node in the graph.

Examples
--------
>>> G = nx.complete_graph(5)
>>> sorted(nx.common_neighbors(G, 0, 1))
[2, 3, 4]
"""
if u not in G:
raise nx.NetworkXError('u is not in the graph.')
if v not in G:
raise nx.NetworkXError('v is not in the graph.')

# Return a generator explicitly instead of yielding so that the above
# checks are executed eagerly.
return (w for w in G[u] if w in G[v] and w not in (u, v))